LTL formulae and Büchi automata
The global motion task that the robot team should fulfill is specified as an \(LTL_{-X}\)  formula [1]}, [2]}. The subclass of LTL denoted as \(LTL_{-X}\)  contains formulae recursively defined over a set of atomic propositions \(\mathcal {Y}\) , by using the standard Boolean operators (\(\lnot \)  - negation, \(\wedge \)  - conjunction, \(\vee \)  - disjunction, \(\Rightarrow \)  - implication, and \(\Leftrightarrow \)  - equivalence) and some temporal operators (\({\cal U}\)  - until, \(\diamondsuit \)  - eventually, and \(\square \)  - always). For simplicity of notation we further write LTL instead of \(LTL_{-X}\) , the difference being the absence of the next operator \(\bigcirc \)  in \(LTL_{-X}\)  [3]}, [4]}, [2]}.
